www.walsaip.uprm.eduWALSAIP

SAR Imaging Radar System

A fundamental problem in designing a SAR Image Formation System is finding an optimal estimator as an ideal impulse response function. As future work, an efficient estimator should be designed, and processed in a second two-dimensional linear convolution with the raw data generated as output of the SAR Imaging Radar System. This will be done in order to obtain a precise estimator function of the Earth’s surface, providing a proper, detailed image formation.

Problem Formulation1

Basic SAR Characteristics2

Future Work6

Conclusions 5

Theoretical Framework3

SAR Implementation Results4

Acoustical Map:

Abigail Fuentes – M.S. Student Prof. Domingo Rodriguez – AdvisorAIP Group, ECE Department, University of Puerto Rico, Email: abigail.fuentes@ece.uprm.edu Mayagüez Campus

Synthetic Aperture Radar (SAR) Signal Processing Algorithms for Raw Data Generation and Image Formation

Supported ByA I PGroupGroupA u t o m a t e dI n f o r m a t i o nP r o c e s s i n g

2

The SAR Image Formation System deals with obtaining an optimal, detailed image of the Earth’s surface from the raw data generated by the SAR Imaging Radar System.

Institute for Computing and Informatics Studies

DRNA

How to develop computationally efficient algorithms to model Synthetic Aperture Radar Signal Processing Systems.

Figure 1: SAR System

SAR is a form of radar designed to be used aboard moving instruments, such as an aircraft or satellite, over large and relatively immobile targets located at the Earth’s surface. A SAR system should be developed in order for these moving instruments to acquire clear and precise images of the different targets positioned at the Earth’s surface.

For this work, a SAR System was implemented in MATLAB, and a satellite image of Arecibo, Puerto Rico (256 X 256 pixels) was used as the input function describing the Earth’s surface.

The impulse response function of a SAR System is modeled as a discrete cross-ambiguity function between a transmitted signal and received signal as follows:

To obtain an input function that describes the Earth’s surface, the SAR radar (see figure 2) transmits a series of pulses at a fixed repetition rate. These pulses hit reflectors located at the Earth’s surface. The pulses returned from the reflectors are collected and form a discrete reflectivity density function of the Earth’s surface.

The output of the SAR Imaging Radar System represents the raw data generated, and is computed as the two-dimensional linear convolution between the impulse response function and the discrete reflectivity density function.

Figure 2: Impulse Response Function Generation

Figure 3: SAR Imaging Radar System

SAR Image Formation System

SAR Imaging RadarSystem

h (mx , my)

ρ [n0 ,n1 ] y [n0 ,n1 ]

Figure 4: Proposed SAR System

Raw Data Generated using a chirp signal

50 100 150 200 250 300 350 400 450 500

50

100

150

200

250

300

350

400

450

500

Raw Data Generated using a pulse signal

50 100 150 200 250 300 350 400 450 500

50

100

150

200

250

300

350

400

450

500

The following images obtained from MATLAB present raw data computed by the SAR Imaging Radar System for two types of signals, which were used to generate the cross-ambiguity function as the impulse response function of the system.

Chirp Signal

Pulse Signal

The image of the cross-ambiguity function in terms of the chirp signal resulted to have a distinguishable, single maximum peak. As an optimal estimator for the SAR Image Formation System, the impulse response function in terms of the chirp signal can be approximated as a delta function. However, for the impulse response function computed in terms of the pulse signal, the resulting image presented a wide triangular shape. Hence, a single maximum peak could not be detected.

Raw Data Generated using a chirp signal

50 100 150 200 250 300 350 400 450 500

50

100

150

200

250

300

350

400

450

500

ρ (mx , my) h (mx , my) ĥ (mx , my)

Earth’s Reflectivity Density Function

δ (mx , my)

h (mx , my)

sT(t) sR(t)

Impulse Response Function Generation

ρ (mx , my)δ (mx , my)

Imaging Radar (LSI System) Filter T

h (mx, my) ∆= Impulse Response Function δ (mx, my) ∆= Impulse Function y (mx, my) ∆= Raw Data Function

y (mx , my) = ρ (mx , my)*h (mx , my)

h (mx , my)

r (mx, my) ∆= Noise function

g(mx , my) = y (mx , my) + r (mx , my)

Image Formation System (LSI) System)Filter Ť

ρ^ (mx , my) = g (mx , my) *ĥ (mx , my)

δ (mx , my)

h (mx , my) sT(t)

sR(t)

Impulse Response Function Generation